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User blog:Alzrius/Beauty and Blades: A Thought Experiment
Queen's Blade - a tournament whereby the strongest and most beautiful fighters compete to become the next Queen. The above sentence is often spoken in the Queen's Blade anime as a basic summary of what the series is about. However, those who watch the series will be aware that this signature phrase is slightly inaccurate. There is no contest nor competition with regards to the beauty of those competing for the throne. Indeed, the beauty of whomever happens to become the next Queen is, insofar as the tournament progression is concerned, completely incidental. While the tournament proper doesn't concern itself with the beauty of its contestants, its interesting to consider what changes would need to be made if it did. That is, what would the Queen's Blade tournament be like if it made beauty, as well as martial prowess, a factor in the competition? Let's see if we can answer that question here. Rules in Review Before we look at changing the structure of the tournament, let's take a moment to review the rules and structure of the tournament as it currently is. Note that most of this information can be found over on the tournament's wiki page as well. The first major point of note is that the tournament varies wildly in how its conducted across various Queen's Blade media. In the anime, the tournament is administrated by angels, and images of each fight are broadcast via appearing on the moons. While the ostensible purpose of the tournament is to choose the next Queen, it seems that its actual goal (at least insofar as the angels who run the tournament are concerned) is to put into power a Queen who will keep the Marshland Witch in check; this is stated very boldly by Laila (relaying a message from Nanael) to Queen Claudette near the end of the Rebellion anime. Unfortunately, the anime's presentation of the actual tournament is largely a mess. We're not told of any rules of entry or conduct, for example. Much worse, the actual structure of the tournament appears to be ad hoc at best. Thoughout the initial series (Rurou no Senshi/"The Wandering Warrior"/"The Exiled Virgin") various fights happen under the auspices of being Queen's Blade matches, but nothing seems to come of them. Fighters who previously lost matches reappear in the subsequent series (Gyokuza o Tsugumono/"Those Who Seek the Throne"/"The Evil Eye") to fight again, with no apparent rhyme or reason for how they can continue to fight, or whom they'll be fighting. The only notable point we're given about the tournament's format is that it's held every four years. By contrast, the other Queen's Blade media present a much more coherent picture of the tournament. This is presented primarily in the Hide & Seek manga, with a few additional materials presented in other sources. As in the anime, the tournament is held every four years. However, there are no angels involved in its administration; the entire tournament is completely terrestrial how it's run. Each fight is still broadcast to the general populace, but in crystal balls that are small enough to be held in the palm of one's hand. We're also told that the tournament's bracket - which is shown to be of a single-elimination style - is created by the current Queen, in secret, with each match being publicly announced three days prior. The actual process of running the tournament is handled by the royal mages. Helpfully, we're also told about the tournament's rules of entry and rules of conduct. The rules of entry are the guidelines by which a potential contestant must meet in order to attempt to enter the Queen's Blade tournament. Each applicant must: * Be female. * Be of sound mind. * Be at least twelve years of age. It's worth noting that these restrictions are broad enough that they don't seem to require any particular degree of enforcement. While there could potentially be some sort of question as to a young (or young-looking) candidate's age - or even to her sanity - it seems more likely that these rules function largely to restrict entries from candidates that lack the capacity to function as Queen. One other rule of entry exists: that those who satisfy the above conditions must pass a preliminary round of competition in order to be entered into the tournament proper. This is a point worth noticing, and one we'll return to shortly. For those that pass the preliminary round and participate in the tournament itself, there is only one rule of conduct: killing your opponent is forbidden. While the penalty for those rule is unstated, it's reasonable to assume that those who break this rule are disqualified from the tournament. Given that the manga and related media present the Queen's Blade tournament in a much more coherent fashion, the remainder of this article will use this as the default assumption for how the tournament functions. Structural Integrity It was mentioned above that Queen's Blade functions as a single-elimination tournament. This deserves some closer examination, because the number of rounds for a single-elimination tournament is always generated as a binary logarithm (which gives us, by extension, the total number of matches for each round and for the tournament as a whole). As the tournament includes a final match against the reigning Queen, this final number (for both the total number of rounds and the total number of matches) is increased by one. It's at this point that we turn our attention to the 30th Queen's Blade tournament, the one depicted in the various Queen's Blade media as the one that Leina participated in. This tournament had a grand total of eighteen participants (Shizuka is not counted as one of these, as she does not enter the tournament proper in any media). This is problematic, as eighteen has no binary logarithm (as an integer, that is), and so this would throw off the structure of the tournament bracket. Now, it's entirely possible to have a tournament bracket that's asymmetrical in structure, but for the sake of simplicity (and presumably the sake of fairness towards the competitors, rather than making some of them fight extra matches) we'll try and reduce the number of fighters down to sixteen, that being the closest number that has a binary logarithm. As it turns out, this is surprisingly easy to do. The first step is to remove Queen Aldra from the roster. This is because, as the reigning Queen, she does not have to participate in the tournament bracket; instead, her only fight is in the final match against the last competitor standing, which we know was Leina. This brings us down to seventeen competitors. Absence of Irma A strictly canonical reading of the events of Queen's Blade, in any of its media incarnations, holds that all seventeen participated in the tournament proper. While its troublesome to reconcile, I'd propose an alternative theory - that Irma did not officially participate. The reason for this theory on my part is one of internal logic within the context of the narrative. As one of the Queen's Fang Assassins, Irma's mission is ostensibly to covertly eliminate any fighters in the tournament that could conceivably defeat Queen Aldra, presumably in her disguise as being a mere cleaning lady. In fact, her actual mission (known only to herself) is to kill the Queen. These points are notable because formally entering herself in the tournament runs directly counter to achieving them. Entering the tournament would not only broadcast Irma's identity to the world - including all of her potential targets, making any attempts at assassination much more difficult - but would also place her directly on a course to fight the Queen, which also runs counter to the idea of a covert coup. As such, I propose that Irma never officially appeared on the tournament bracket for the 30th Queen's Blade competition, leaving a grand total of sixteen fighters, which perfectly fill the available slots. Quantified Guesswork Using the above reasoning, we know that the 30th Queen's Blade tournament had sixteen official competitors, not including Queen Aldra. As the binary logarithm of sixteen is four, we know that the tournament had five rounds (due to Queen Aldra being a +1). What we don't know is if this number is standard for each instance of the Queen's Blade tournament, or if each tournament's size adjusts to the number of qualifying competitors. While there's no way to be certain, we can presume that each Queen's Blade tournament uses the above structure (that of allowing no more than sixteen qualifying participants over a total of five rounds) due to the mediocrity principle. That is, in absence of evidence to the contrary, we presume that this tournament is not unlike any other tournament in any given way. More specifically, we're presuming that the sixteen available slots in the 30th tournament are due to that being a static number of participants allowed, rather than sixteen just happening to be the total number of fighters who qualified after the preliminary matches. In this case, that would mean that the preliminary matches function to reduce the pool of potential competitors down to sixteen. A Note on Nomenclature On a slight tangent, it's worth noting that a strict reading of the tournament bracket under the binary logarithm that generated would place the final match - the one where the sole remaining contender faces the Queen - as being outside of the Queen's Blade tournament proper. To put it another way, the terminology of a single-elimination tournament holds that the round when there are sixteen competitors (which is the first round of Queen's Blade) is the eighth-finals. Following that is the quarter-finals (when there are eight competitors), then the semi-finals (when there are four competitors), and then the finals (when there are two-competitors, which in the case of the 30th Queen's Blade tournament were Leina and Claudette). A strict interpretation of this would mean that the Queen's Blade tournament is not, per se, to determine who will become the next Queen. Rather, the tournament is a competition to see who will win the right to challenge the existing Queen for her throne. A character that wins Queen's Blade, therefore, is only guaranteed of the opportunity to try and become Queen. She could still lose the subsequent match against the reigning Queen. (On a slightly more sinister note, if this last match is outside of the tournament proper, then it could very well mean that killing your foe is permissible. In that case, it might explain why we never see the woman who was Queen prior to Aldra...) Of course, the Queen's Blade media universally refers to Claudette as having been eliminated in the "semi-finals," despite her having been in what were technically the finals. As such, it seems clear that the people of Queen's Blade consider the fight against the Queen to be part of the tournament structure. Battle of the Beauties It's here that we turn our attention back to the original subject of this article, namely the manner in which the tournament would concern itself with adding beauty as an area of competition between the participants, while still maintaining its martial aspect. Of key importance is the preliminary match by which an applicant earns the right to appear on the tournament bracket. Presenting the Preliminaries The only media to show the preliminary matches in any regard is the Exiled Warrior manga, where we witness Leina defeat Linshang in her preliminary match, qualifying for the tournament as a result. In this presentation, there's virtually no difference between the preliminary matches and the tournament proper. Both are one-on-one combat sessions where the winner advances to the next round of fighting. Taken the previous reasoning into account, however, this leaves some unanswered questions as to how the preliminary matches function. More specifically, if we presume that there are only sixteen available slots in the tournament proper, and that the preliminaries are a single round of combat (since we never see anything to indicate otherwise - if there were multiple rounds of preliminaries, we'd essentially have a tournament to qualify for the tournament) where the winner qualifies and the loser is disqualified, then what happens when there are more than thirty-two women who want to participate in Queen's Blade? Simply put, the preliminaries need to do more than just halve the pool of potential applicants. That's where the idea of using beauty as a qualifying factor comes into play. Miss Continent The idea here is to add an intermediate step between the preliminary matches and the tournament proper. In this phase of the competition, after the preliminary matches have served to eliminate half of the applicants, those who won their preliminary matches are then ranked based on their appearance, with the sixteen most beautiful fighters then moving on to the actual Queen's Blade tournament itself. The question that this immediately raises is what methodology is used to determine beauty among the contenders. Because of the subjective nature of what constitutes beauty, let alone which woman is more beautiful than the others, the best method would probably be one of general consensus - that is, it would be determined by popular vote. This, however, requires further explanation. As with any question of democratic determination, we need to consider three aspects: who is allowed to participate, how is the ballot constructed, and how are the results determined? We'll go over each of these in turn. The Voters Simple logistics would likely restrict voting to those already in and around Gainos. Because the Queen's Blade tournament is administrated by the royal mages - who have no actual magical abilities - and because the competitors can't be determined until after the preliminary matches are over, it's likely to be too impractical to send ballots all over the Continent and then collect them, particularly in anything resembling a timely fashion. As such, only the people of Gainos are allowed to vote. While we don't have enough information to suggest what if any restrictions would be placed on the eligibility of the population of Gainos, we can make some presumptions about the size of the voting pool. The world of Queen's Blade has several resemblances to medieval Europe. As gunpowder-based weapons exist only as rare artillery weapons (e.g. the cannon's on Lilianna's ship), with personal firearms not having been invented yet, this is roughly equivalent to the mid-14th century. Using that as a guideline, we can judge Gainos's population as being roughly equivalent to that of a major European population center at the same time. As the population of London was around 50,000 in the year 1350, we'll presume that that's the population of Gainos. Ergo, that's also the size of the voting population. Except, that's slightly too simple. For one thing, there are going to be those that can't vote, simply due to age or infirmity, alongside whatever eligibility factors may exist. In contrast, we're also going to assume that the city's population swells when the Queen's Blade tournament happens (spectators, merchants, etc.) and that these transient residents are likewise allowed to cast their votes. Purely for the sake of simplicity, we'll assume that the population of Gainos during the Queen's Blade tournament increases to the point where, even after removing those who can't vote for the reasons mentioned previously, the total voting population is around 100,000, or twice that of the city's normal size. The Ballot As this particular election is requires ranking multiple candidates, and is set to fill sixteen slots simultaneously, the method by which votes are cast will almost certainly use the single transferable vote. This simply requires that the ballot list all applicable candidates (which, in this case, is every fighter that won her preliminary match) and numerically rank them in order of whom each voter finds most beautiful. While the linked page describes the intricacies of the system, the basic way it works is that a candidate only needs a certain number of votes to be elected to a slot (rather than requiring a plurality), and that once that threshold has been achieved, any excess votes are transferred to the second-choice candidate - if that candidate has achieved the number of votes to reach the threshold, then the vote goes to the third-choice candidate, etc. The Results The remaining question then becomes how many votes are necessary to be elected to one of the sixteen slots in the tournament bracket. As we've already established that 100,000 voters are voting for sixteen slots, it would seem natural to divide the former by the latter, and say that each candidate needs to achieve 6,250 votes to be elected. However, this system - known as the Hare Quota - is less than optimal. This is because this sets the bar high enough that, presuming a large enough field of candidates, it's entirely possible to spread the votes so thin that some slots aren't filled. While such a scenario is not unsolvable - perhaps the candidates that come the closest are simply given the remaining slots, or perhaps there's a run-off of some kind (such as by transferring the votes for the candidate with the fewest votes to the secondary choices, etc.) - it's burdensome enough that we'll want to try and avoid it altogether. As this is the outcome setting the vote threshold too high, we'll need to lower it. Another possibility is the Hagenbach-Bischoff Quota, which sets the threshold at slightly lower as being the total number of votes available divided by the total number of slots plus one. In this case, that would be 100,000 divided by seventeen, rather than by sixteen. Rounding the fraction up, this would require only 5,883 votes to qualify. However, while this does lower the threshold for qualifying by a not-inconsiderable amount, this is also less than optimal. The problem is that, while it's unlikely, this number can theoretically result in more candidates being elected than there are seats to be filled. The answer to this is to use the Droop Quota, which functions identically to the Hagenbach-Bischoff Quota, except that it adds one to the result of dividing the available votes by the number of available slots plus one. To put it another way, this would require a threshold of 5,884 votes to be elected to a seat. That may seem like a trivial difference, but it makes it mathematically impossible to elect more candidates than there are seats available to be filled (though in theory, ties are still possible). Game-Changing The notable change here is that this changes the preliminary matches from simply being a qualifying match to being a qualifying match and an exhibition match at the same time. While that sounds fairly mundane, it has notable implications for how the preliminaries would be handled. Specifically, it wouldn't be enough to win; rather, a fighter would need to win and to look good doing it, since the preliminaries are where potential voters would be able to see a fighter in action, and decide which beauties they wanted to vote for. More practically, this offers an explanation for why the women of Queen's Blade dress like strippers. While their outfits are highly impractical in a fight, they're exactly the sort of clothes that would earn them votes in the subsequent election. If we presume that there's another rule of conduct for the tournament proper that says that participants must wear the same outfit in Queen's Blade that they wore during the preliminaries - presumably to eliminate any unfair advantages, such as a fighter dressing skimpily during the preliminaries (when she's statistically more likely to face a weaker opponent), only to change into thicker armor during the tournament proper...though really this rule would likely be so that the people can continue to watch women fighting while scantily-clad - then this would further explain why they keep wearing so little during the remainder of the tournament. If we take this presumption a step further, it would even explain why they show so much skin even prior to entering the tournament. In that case, showing themselves off while wearing signature skimpy outfits would be, in essence, campaigning for votes before the preliminaries are even held. They'd be building popularity via recognition. For those of us who enjoy the series, of course, the sexy outfits need no such justification. But from an in-character standpoint, this would be a nice explanation for how it is that the strongest among the most beautiful becomes the Queen. Category:Blog posts